It looks like Nassau may be circling back to Nassau University Medical Center to once again provide medical care to county jail inmates. It could make sense, given that the hospital is the jail’s next-door neighbor.

Negotiations with NUMC also make sense because, should Armor Correctional Services, as it has promised, stop providing medical care next month, jail emergencies will end up going to the closest hospital — NUMC — anyway.

That’s something NUMC — which for years has been improving its facilities and services in an attempt to distance itself from its reputation as a hospital that primarily served the poor — certainly would not want.

And it’s a scenario that NUMC, which already is struggling with its finances, would not need.

Nonetheless, the hospital is finding itself caught in the middle of a dispute between Nassau and its vendor, Armor, which has notified Nassau of its intent to leave when its contract expires May 31.

Under its contract with Nassau, Armor is supposed to stay on site through June and July to aid the transition to a new vendor.

Armor has gone to court seeking a judgment that would allow it to leave once its contract expires on May 31. And Nassau, in response to Armor’s court filings, acknowledges that it has received no bids from qualified replacement vendors.

In the years since, as both Nassau’s comptroller and the county legislature’s independent office of budget review have noted, the county saved millions of dollars by using the private vendor.

But the cost of handling lawsuits arising over the quality of medical care could blunt some of those savings. The county and Armor lost the first case to go to trial in federal court, in which the family of a Iraq War veteran who committed suicide at the jail won almost $8 million.

As of now, NUMC looks to be the only viable option for the jail, which under law must provide inmate care.

“We are in discussions with Nassau County relative to developing a temporary contingency plan for this urgent situation and cannot comment further, pending the outcome of these discussions,” said NUMC spokeswoman Shelley Lotenberg said Tuesday. Brian Nevin, spokesman for County Executive Edward Mangano, said Nassau “is working on a contingency plan with NUMC and the term is under negotiations.”